Question

If ax2 – 7x + c has 14 as the sum of the zeroes and also as product of the zeroes,
find the value of a and C.
anybody please answer correctly ​fastttttttt.....

Answer 1

Given :

ax² - 7x + c has 14 as the sum of the zeroes and also as the product of the zeroes.

To Find :

Find the value of a and c

Solution:

As we know that :-

α + β = -b/a

→ 14 = -(-7)/a

→ 14a = 7

→ a = 7/14

→ a = 1/2

And

αβ = c/a

→ 14 = c ÷ 1/2

→ 14 = 2c

→ c = 14/2

→ c = 7

Hence,

The value of a is 1/2 and c is 7

Verification :-

→ ax² - 7x + c

→ x²/2 - 7x + 7

→ x² - 14x + 14/2 = 0

→ x² - 14x + 14 = 0

here,

a = 1

b = -14

c = 14

By using quadratic formula we factorise this

x = -b ± √b² - 4ac/2a

→ -(-14) ± √(-14)² - 4×1×14/2(1)

→ 14 ± √196 - 56/2

→ 14 ± √140/2

→ 14 ± 2√35/2

As we know that :-

sum of zeroes = 14

→ 14 + 2√35/2 + 14 - 2√35/2 = 14

→ 14 + 2√35 + 14 - 2√35/2 = 14

→ 28/2 = 14

→ 14 = 14

LHS = RHS

And

αβ = 14

→ 14 + 2√35/2 × 14 - 2√35/2 = 14

→ 196 - 140/4 = 14

→ 56/4 = 14

→ 14 = 14

LHS = RHS

Hence,

Verified

It shows that our answer is absolutely correct.

Answer 2

$\large\underline\mathrm{Given:-}$

ax² – 7x + c has 14 as the sum of the zeroes and also as product of the zeroes.

$\large\underline\mathrm{To \: find}$

Find the value of a and c.

$\large\underline\mathrm{Solution}$

$\alpha + \beta = - b \div a$

$\implies$ 14 = -(-7)/a

$\implies$ 14a = 7

$\implies$ a = 7/14

$\implies$ a = 1/2

$\alpha \beta = c \div a$

$\implies$ 14 = c/(1/2)

$\implies$ 14 = 2c

$\implies$ c = 7

$\implies$ ax² - 7x + c

$\implies$ x²/2 - 7x + 7

$\implies$ x² - 14x + 14/2 = 0

$\implies$ x² - 14x + 14 = 0

here,

$\implies$ a = 1

$\implies$ b = -14

$\implies$ c = 14

By using quadratic formula we factorise

$\implies$ x = -b (-,+)√b²-4ac/2a

$\implies$ -(-14)(-,+)√(-14)²-4×1×14/2(1)

$\implies$ 14 (-,+)√(196-56/2)

$\implies$ 14 (+,-)√140/2

$\implies$ 14 (-,+)2√35/2

Sum of zeroes = 14

$\implies$ 14 + 2√35/2 + 14 - 2√35/2 = 14

$\implies$ 28/2 = 14

$\implies$ 14 = 14

$\implies$ L.H.S = R.H.S

$\alpha \beta = 14$

$\implies$ 14 + 2√35/2 × 14 - 2√35/2 = 14

$\implies$ 196 - 140/4 = 14

$\implies$ 56/4 = 14

$\implies$ 14 = 14

$\implies$ L.H.S = R.H.S